* Corresponding author. Tel.: #886-3-5731880; fax: #886-3-5727835. E-mail address: [email protected] (C.-J. Tsai).
Institute of Environmental Engineering, National Chiao Tung University, No. 75 Poai St., Hsin Chu, Taiwan
Institute of Occupational Safety and Health, Council of Labor Awairs, Taipei, Taiwan Received 10 March 2000; received in revised form 28 December 2000; accepted 7 January 2001
Abstract
This study has investigated numerically the particle collection e$ciency of an impactor with porous metal substrates. Two-dimensional #ow "eld in the inertial impactor was simulated by solving the Navier}Stokes equations with the control volume method. Particle trajectories were then calculated to obtain the collection e$ciency at di!erent Reynolds numbers, which are based on nozzle diameter, and at di!erent K, which is the resistance factor of the porous metal substrate. This study shows that some air may penetrate into the porous metal substrate resulting in di!erent particle collection e$ciency than that predicted by the traditional theory. The particle collection e$ciency for the impactor with the porous metal substrate is higher than that with the #at plate substrate below the cutpoint, and numerical results are in good agreement with the experimental data. The dimensionless parameter"(;/2Kt)(D/=) has been introduced to deter-mine the excess particle collection e$ciency,, by the porous metal substrate in the limit of (StP0. The theory explains the experimental data of the excess collection e$ciency very well. 2001 Elsevier Science Ltd. All rights reserved.
Keywords: Collection e$ciency; Porous metal substrate; Inertial impactors
1. Introduction
This study was conducted to investigate the e!ect of air penetration into the porous metal substrate on the particle collection e$ciency of an impactor with porous metal substrates.
0021-8502/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 8 5 0 2 ( 0 1 ) 0 0 0 3 8 - 6
Fig. 1. The schematic diagram of an impaction stage with porous metal substrate (S: jet-to-plate distance; ¹: nozzle throat length; D: diameter of porous metal substrate).
Inertial impactors are widely used for size-fractionated sampling of aerosols. Theoretical analysis of the inertial impactors predicted the cuto! diameter and the shape of the collection e$ciency curves reasonably well for the liquid particles. Hard solid particles may bounce o! the collection substrates of the inertial impactors. Surface coating on the collection substrate is often used to reduce particle bounce. The porous metal disc impregnated with mineral oil has also been used as an impaction substrate to prevent particle bounce (Reischl & John, 1978; Marple & McCormack, 1983; Turner & Hering, 1987).
The use of uncoated substrate as a collection surface is suitable for subsequent chemical and elemental analysis of the collected particles because it is free of interference from coating materials (Biswas & Flagan, 1988). Newton, Carpenter, Cheng, Barr, and Yeh (1982) used the uncoated stainless steel substrates in the cascade impactor for sampling aerosols in the exhaust gas of the pressurized #uid bed coal combustion system at high temperature and pressure. However, the uncoated porous metal substrate has not previously been used as collection surface for inertial impactors, therefore, there is very little information available on the particle collection e$ciency. In our previous study (Tsai, Huang, Wang, & Shih, 2001), a 2 l/min personal denuder consisting of a two-stage impactor, and two denuder discs has been developed. The cuto! aerodynamic diameter is 9.5 and 2.0m, and the nozzle diameter is 0.72 and 0.19 cm for the"rst and second stages, respectively. The schematic diagram of one stage of the impactor is shown in Fig. 1. Uncoated porous metal discs (diameter: 1.2 cm, pore size: 100m, thickness: 0.317 cm, P/N 1000, Mott Inc., Farmington, USA) are used as the impaction substrates in the impactor. The experi-mental results indicate that the maximum particle loss by the downstream denuder is less than 9% for particle aerodynamic diameter smaller than 2.0m. Loss can be much higher for larger particle sizes. Since particles larger than 2.0m are removed by the cascade impactor, particles collected by the downstream denuder are not expected to interfere with gas concentration measurement. In the loading test, the experimental results indicated that the uncoated porous metal substrate prevents particle overloading problem because of its capillary action. If a #at plate substrate was used, impacted liquid particles were found to coalesce into a single droplet and subsequently reentrained. Two extra stages with the nozzle diameter of 0.26 and 0.36 cm, respectively, were later built and their particle collection e$ciencies were also determined using monodisperse oleic acid test particles as described in Tsai and Cheng (1995). Test results indicated that discrepancy between the experimental data of Tsai et al. (2001) and theoretical results of Marple (1970) for solid substrates on particle collection e$ciency exists as shown in Fig. 2, where the Stokes number St"Cd;/9=
Fig. 2. Experimental data and theoretical results (Marple, 1970) of the particle collection e$ciency.
(C: Cunningham slip correction factor;: air viscosity; : particle density; d: particle diameter; ;: air velocity at the nozzle; =: nozzle diameter). Instead of a sharp collection e$ciency curve as predicted by Marple's theory, there are tails at the bottom of the curves. The collection e$ciency does not seem to go to zero when the Stokes number goes to zero, especially for the small nozzle diameter of 0.19 cm. This disagreement was due to excess particle collection resulting from air penetrating into the porous metal substrates. This phenomenon was found by Rao and Whitby (1978) for the "lter substrates. Their experimental results indicated that the performance of impactors was signi"cantly a!ected by the nature of the collection surface. The glass "ber "lter used as an impact collection surface reduced the particles bounce, but altered the shape of the e$ciency curve. For example, at low stokes numbers for which the oil-coated glass plate had zero or low collection e$ciency, the e$ciency of the glass "ber "lter was much higher than that of the oil-coated glass plate. One of the probabilities of the increase in the collection e$ciency was thought to be attributed to the aerosol jet penetration into the "lter surface.
To facilitate the design of the impactor with the porous metal substrates, the particle collection e$ciency characteristic was investigated using numerical models which calculate #ow "eld, particle trajectories and collection e$ciency. The theoretical collection e$ciency curves were then com-pared with the experimental data. An asymptotic theory was developed to describe the excess particle collection e$ciency in the limit of (StP0.
2. Numerical method
The #ow "eld in the inertial impactor was simulated by solving the 2-D Navier}Stokes equations in the cylindrical coordinate. The #uid #ow in the impactor was assumed steady, incompressible and laminar, and air was assumed to be at 203C and 1 atm. The governing equation was discretized
Fig. 3. Main control volume distribution for the #ow "eld calculation in the present study. (Hatched area is the porous metal substrate.)
by means of the "nite volume method and solved by the SIMPLE algorithm (Patankar, 1980). One example of the calculation domain is shown in Fig. 3, where the number of grids is 40,000 (200 in r-direction ;200 in z-direction). The#ow "eld is governed by
(V')V"!P#V!KV, (1)
where the last term of the right-hand side of the above equation is the additional pressure drop for the #uid #ow through the porous metal substrate based on the Darcy's law. In Eq. (1) V is velocity vector in cm/s; P the pressure in dyne/cm; the air density in g/cm; K the resistance factor of the porous metal substrate in cm\ (K"I, k is the permeability).
After obtaining the #ow "eld, the particle equations of the motion were solved numerically to obtain particle trajectories and collection e$ciency. The particle equations of motion in r (radial) and z (axial) directions are
mduPdt "CRed8C (uP!uP), (2)
mduXdt "CRed8C (uX!uX)#mg. (3)
In the above equations, C is the empirical drag coe$cient; Re the particle Reynolds number; m and g the particle mass and the gravitational acceleration, respectively; uP and uX the particle velocities; uP and uX local #ow velocities in the radial and axial directions, respectively.
Fig. 4. The particle collection e$ciency curves for the impactor with the porous metal substrate at di!erent numbers of grids.
the nozzle, and particles are assumed to be collected when they hit the porous metal substrate, then the collection e$ciency can be calculated as
"(r/(=/2)), (4)
where r is the critical radius across the nozzle within which particles will be collected. For comparison, the #ow "eld and the particle collection e$ciency for the impactor with #at plate substrates were also simulated.
3. Results and discussion
3.1. Ewect of number of grids on the collection ezciency
Fig. 4 shows the particle collection e$ciency curves for the porous metal substrate with K" 568,000 cm\ at the#ow rate of 2 l/min based on di!erent number of grids. As the number of the grids increases from 40,000 to 90,000, the collection e$ciency curves do not change and almost overlap with each other. Hence in the subsequent simulation, 40,000 grids were used.
Fig. 5. Comparison of numerical results with experiment data (Tsai et al., 2001) for the collection e$ciencies of oleic acid particles.
3.2. Comparison of numerical results with experimental data
The calculated collection e$ciencies of the impactor with the porous metal and #at plate substrates are compared with the experimental data and shown in Fig. 5. It is seen that the particle collection e$ciency for the impactor with the porous metal substrate is higher than that of the impactor with the #at plate substrate. The former is in much better agreement with the experi-mental data. In the limit of small particle diameter, the particle collection e$ciency does not go to zero because some air #ow penetrates into the porous metal substrate, as shown in both the experimental data and the present numerical study.
3.3. Ewect of Re on collection ezciency curves
The particle collection e$ciency curves of the impactor with porous metal substrate is shown in Fig. 6 at di!erent Reynolds numbers, Re, where Re is based on the nozzle diameter. Also shown in Fig. 6 is the theoretical collection e$ciency curve of Rader and Marple (1985). It is seen that the curve is in very good agreement with that calculated in this study assuming the #at plate substrate. Compared to the case of the #at plate, there is a substantial shift of collection e$ciency curves to the left for the case of the porous metal substrates. As Re is increased, the curve becomes less sharp and deviates more from the traditional theory, which is based on the #at plate substrates. In the limit of (StP0, the collection e$ciency does not go to zero and is called the excess particle collection e$ciency, . When Re is increased, increases and (St (Stokes number at 50% collection e$ciency) decreases.
Fig. 6. The particle collection e$ciency curves at di!erent Reynolds numbers. Nozzle diameter"0.19 cm,
K"568,000 cm\.
Fig. 7. The particle collection e$ciency curves at di!erent K. Nozzle diameter"0.19 cm, Re"1500.
3.4. Ewect of K on collection ezciency curves
Fig. 7 shows the in#uence of K on the particle collection e$ciency for the impactor with the porous metal substrates at Re"1500, nozzle diameter ="0.19 cm. It is seen that the particle collection e$ciency increases as K is decreased at the same(St. In the limit of (StP0 the excess particle collection e$ciency also increases with a decreasing K. This is because that more air penetrates into the porous metal substrate when K is smaller. As K is as large as 10 cm\, the
Fig. 8. The in#uence of Re, K and = on the excess particle collection e$ciency.
collection e$ciency curve is close to that of the #at plate substrate, and the excess particle collection by the porous metal substrate can be neglected. For the porous metal substrate, the resistance factor increases with decreasing nominal pore size. For example, the resistance factor of porous metal substrate with 5m pore size and 0.157 cm thickness will be as high as 1.2;10 cm\ (Heikkinen & Harley, 2000). Therefore, there will be negligible excess particle collection e$ciency in this case.
Fig. 8 shows the e!ect of the Reynolds number, resistance factor and nozzle diameter on the excess particle collection e$ciency for the impactor with the porous metal substrate. Beside the factor K which in#uences very much, it is seen that both Re and = are also important factors in#uencing. When Re is larger, the thickness of the boundary layer over the substrates is thinner, the air #ow penetrate into the porous metal substrate more easily resulting in a higher particle collection e$ciency at any "xed K and =. When K is smaller than 10 cm\, increases drastically with a decreasing K at any "xed Re and =. The excess particle collection e$ciency is found to be smaller for the case with a larger nozzle diameter at any "xed Re and K. At the same Re, the dynamic air pressure will be larger for the case of a smaller nozzle diameter than that of a larger nozzle diameter. The area over which air penetrates into the substrate relative to the nozzle area becomes larger for the case of the smaller nozzle diameter, leading to a higher excess collection e$ciency.
3.5. Asymptotic theory of excess particle collection by porous metal substrate
To model the e!ect of various factors on the excess particle collection by the porous metal substrate, the pressure drop for the air penetrating through the porous metal substrate is assumed to be proportional to the dynamic pressure of the #uid #ow in the nozzle as
Fig. 9. The relationship between the excess particle collection e$ciency and the dimensionless parameter. Symbols represent numerical results and the dashed line is the "tted curve.
where is a proportionally constant, t the thickness of the porous metal substrate, ; the average air velocity penetrating into the porous metal substrate.
Assuming that the particle concentration over the substrate surface is the same as that at the nozzle, the excess collection e$ciency of particles can be de"ned as
";A;A, (6)
where A is the part of the substrate area where air is penetrating, and A is the nozzle area. Substituting Eq. (5) into (6), the excess collection e$ciency of particles can be calculated as
"2K;t
D= L", (7)
where the dimensionless parameter"(;/2Kt)(D/=)L. The ratio of A and A is assumed to be proportional to (D/=)L, due to the fact that the area over which air penetrates into the substrate is related to the nozzle area for the di!erent nozzle diameter. Exponent n is obtained from the best "tting of the numerical results with experimental data and found to be 0.9. Fig. 9 shows the relationship between the excess particle collection e$ciency and the dimensionless parameter. It is seen that the excess particle collection e$ciency increases linearly with an increasing, and the asymptotic theory "ts with the numerical results very well. However, there is an additional complication due to "ltration e!ect of the penetrating aerosol particles by the porous metal substrate. This e!ect is not included in this study. It is believed that if the "ltration e!ect is considered, the excess particle collection e$ciency of the impactor with porous metal substrate will be decreased. For collecting particles upstream of a denuder, the sharp cuto! collection e$ciency curves is desired. Thus, if the excess particle collection e$ciency for the impactor is to be kept smaller than 10%, the theory predicts that must be smaller than 0.07.
4. Conclusions
Using the porous metal substrate as the collection surface of an inertial impactor, it has the advantage that high concentration liquid particles can be sampled without overloading problem because of its capillary action. However, some air may penetrate into the porous metal substrate such that extra particles are collected in the substrate resulting in di!erent particle collection e$ciency than that predicted by the traditional theory. A numerical study has been conducted to calculate the collection e$ciency of the impactor and the calculated results agree with the experimental data very well. The particle collection e$ciency of the porous metal substrate depends on the resistance factor of the porous metal substrate K, #ow Reynolds numbers Re, and nozzle diameter =. In the limit of(StP0, the excess particle collection e$ciency increases with a decreasing K, an increasing Re and a decreasing =.
An asymptotic theory has been developed to determine the excess particle collection e$ciency and the theory predicts the numerical results very well. If the excess particle collection e$ciency for the impactor is to be kept smaller than 10%, the theory predicts that the dimensionless parameter must be smaller than 0.07.
Acknowledgements
The authors would like to thank for the "nancial support of the Taiwan Institute of Occupa-tional Safety and Health under Contract No. IOSH88-A105, and the Taiwan NaOccupa-tional Science Council of the Republic of China under Contract No. NSC 88-2211-E-009-030.
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